Civilians desperately trying to get out of the besieged city of Fallujah by attempting to cross the Euphrates River are being gunned down by Islamic State of Iraq and Levant (ISIL) jihadists, reports say.

“An unidentified number of civilians have been shot and killed trying to cross the river,” the Norwegian Refugee Council (NRC) said.

Civilians from Fallujah cross the Euphrates River to escape ISIL. /AP

Some tried to cross the river by climbing into flimsy boats, barrels and even refrigerators, the NRC said on June 5.

Crossing the Euphrates is one of the only ways for civilians to leave the center of Fallujah, which is littered with ISIL booby traps and roadside bombs.

The NRC, which works with refugees and internally displaced Iraqis, said the report is based on interviews with some of those who fled.

“We tried to escape on foot using secret roads. We made it but there were many accidents on the way,” said one woman, who gave her name as Hannah. “There were cases where people ended up dead and many children were lost. It was hard, very hard.”

Some 18,000 civilians have reached displacement camps since Iraqi forces last month began an operation to liberate Fallujah, but the NRC said as many as 50,000 remain, many being used by ISIL as human shields.

Nasr Muflahi, NRC country director, said: “Our biggest fears are now tragically confirmed with civilians being directly targeted while trying to flee to safety.”

“This is the worst that we feared would happen to innocent men, women and children who have had to leave everything behind in order to save their lives,” he said.

On June 5, Iraqi forces reported securing the southern edge of Fallujah, a largely agricultural area.